Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×D541 |
| Fitting | C2×D4×C541 ⋊ C2 |
| Sylow | C541 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D541 |
| commutator, cosocle | C2×C541 | C24 |
| Frattini | C2 | C23×D541 |
| Fitting | C2×D4×C541 | C2 |
| socle | C22×C541 | C23 |
| hypercenter | C2×D4 | D541 |
| hypocenter | C541 | C22×D4 |
| LCS | G ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D541, #100×D541, #102×D541, … |
| maximal normal subgroup of | #99×D541, #100×D541, #102×D541, … |
| maximal quotient of | C2×C22⋊C4×D541, C2×C4⋊C4×D541, C4×D4×D541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 182);